A356530 - OEIS

%I #11 Aug 10 2022 22:34:44

%S 1,1,4,18,156,1020,23040,189000,8462160,174741840,8418513600,

%T 110288455200,26670240273600,364684824504000,46300470369753600,

%U 5169242034644688000,359472799348030368000,7508907247291081632000,6157317530690533823616000

%N Expansion of e.g.f. Product_{k>0} 1/(1 - (k * x)^k)^(1/k^k).

%F a(0) = 1; a(n) = Sum_{k=1..n} A356529(k) * binomial(n-1,k-1) * a(n-k).

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, (1-(k*x)^k)^(1/k^k))))

%o (PARI) a356529(n) = (n-1)!*sumdiv(n, d, d^(n-d+1));

%o a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, a356529(j)*binomial(i-1, j-1)*v[i-j+1])); v;

%Y Cf. A023882, A294462, A356487, A356529.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 10 2022